Caitlin a movie rental card worth $175. After she rents the first movie, the card's value is $172.25. After she rents the second movie, its value is $169.50. After she rents the third movie, the card is worth %166.75. Assuming the pattern continues, which of the following equations define A, the amount of money on the rental card after n rental?

Options

A. `175-2.75n`
B. `2.75n-175`
C. `(175-2.75)n`
D. `(175)/(2.75)n`

Answer

To solve the problem step by step, we will analyze the situation of Caitlin's movie rental card and derive the equation that represents the amount of money left on the card after renting movies.

### Step 1: Identify the Initial Value
The initial value of Caitlin's movie rental card is given as:
\[ \text{Initial Value} = 175 \]

### Step 2: Determine the Amount Deducted After Each Rental
After renting the first movie, the value of the card is:
\[ \text{Value after 1st rental} = 172.25 \]
The amount deducted after the first rental is:
\[ \text{Amount deducted} = 175 - 172.25 = 2.75 \]

After renting the second movie, the value of the card is:
\[ \text{Value after 2nd rental} = 169.50 \]
The amount deducted after the second rental is:
\[ \text{Amount deducted} = 172.25 - 169.50 = 2.75 \]

After renting the third movie, the value of the card is:
\[ \text{Value after 3rd rental} = 166.75 \]
The amount deducted after the third rental is:
\[ \text{Amount deducted} = 169.50 - 166.75 = 2.75 \]

### Step 3: Establish a Pattern
From the calculations, we see that each time Caitlin rents a movie, $2.75 is deducted from the card's value. This deduction is consistent for each rental.

### Step 4: Formulate the General Equation
Let \( n \) represent the number of movies rented. The value of the card after renting \( n \) movies can be expressed as:
\[ \text{Value after } n \text{ rentals} = \text{Initial Value} - (\text{Amount deducted} \times n) \]
Substituting the known values:
\[ \text{Value after } n \text{ rentals} = 175 - (2.75 \times n) \]

### Step 5: Write the Final Equation
Thus, the equation that defines \( A \), the amount of money on the rental card after \( n \) rentals, is:
\[ A = 175 - 2.75n \]

### Conclusion
The equation that represents the amount of money left on Caitlin's rental card after renting \( n \) movies is:
\[ A = 175 - 2.75n \]